Applied Economic Analysis 1

FX forecasting through machine learning techniques

Víctor Margallo Gálvez

SNR: 2016264

ANR: 957881

Content

• Introduction
• Review of literature theories
• Machine learning approach through technical analysis
• Conclusions

Introduction

The forex market plays a key role in daily management of multinational companies operating in different currencies. Its volume surpasses any other market, exceeding the amount of $5 tn per day. Its global centre is located in London, where around 40 per cent of all transactions are executed.

Importance

International trade and global investing nourish and heavily rely on it. Its functioning is critical in order to support imports and exports, and consequently to incentive the exchange of resources and the creation of additional demand of goods and services. Without its current liquidity companies potential would be limited and global economic growth would be damaged.

With this said, investors also benefit from the foreign exchange market. Need of diversification comes with the necesity of currency exchange in many occasions to buy and sell foreign assets and/or securities. Equally, some investors may see currencies as an asset class itself and trade them to generate returns. The latter is precisely what this assignment tries to obtain. Nevertheless, a good prediction of FX rates is of great help to multinational companies entering exchange risks so that they can have an effective hedging to currencies' volatility.

Forex trading

Interactions between dealers occur in a global over-the-counter (OTC) network that connects buyers and sellers. There is no single exchange, however, there is a big interconnectivity between marketplaces. A result of such structure is the difference in rates between banks or market makers that leaves room for arbitrage opportunities, specially in low volume currencies. In this assignment we assume the rates obtained from the data-sources are available prices for those exchanges and that the real application of the results would depend on the platform we trade, and, consequently, on its prices.

In terms of currency distribution in the FX markets:

</tr>

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Source: Triennial Central Bank Survey. Basel, Switzerland: Bank for International Settlements. 2016.

Note: As currencies are pairs, total is 200%.

 

Its fluctuations are caused by factors across countries such as changes in GDP growth, inflation, interest rates, budget and trade deficits or surpluses, substantial M&A activity and other macroeconomic conditions.

In the analysis to come, we will briefly introduce the classical macroeconomic approaches of Relative Purchasing Power Parity (PPP) and the International Fisher effect for interest rates.

Review of literature theories

 

Relative Purchasing Power Parity

PPP theory says that exchange rates are equal to purchasing power ratios between countries. This means that a fall in purchasing power in one currency would lead to a decrease in that currency's price in the FX market. Therefore, we could expect that at par, the product's value would be the same in any currency terms as the exchange rates would adjust to offset differences.

This might be true for easily and cheaply transportable commodities, nonetheless, it does not hold for other goods and services due to distortion of parity caused by transportation costs.

 

$$S=\frac{P_{1}}{P_{2}}$$

Where:

• $S$ is exchange rate of Currency 1 for one unit of Currency 2.
• $P_{1}$ is price of the good in Country 1 and $P_{2}$ is the price in Country 2 in their respective

From this approach, we can evaluate it this theory to see overpriced or underpriced currencies by measuring different baskets of goods.

A classical example of a PPP index is the one from The Economist:

The Big Mac index helps determine over and under priced currencies with respect the US Dollar. It follows PPP theory and argues that if a Big Mac costs $P_{USD}$ in the US and $P_{GBP}$ in the UK then the exchange $USD/GBP$ will be $PPP\space S_{USD/GBP}=\frac{P_{USD}}{P_{GBP}}$. For any $Market\space S_{USD/GBP}>PPP\space S_{USD/GBP}$ we would find the British pound overvalued.

So far, all discussion has been focused on the Absolute PPP. However, in order to predict movement in the exchange rate we have to add variability in prices for the goods and services in the countries. That is why we introduce the Relative PPP, which predicts relationship between inflation rates and the exchange rate.

The reasoning is that the movement in market rates is equal to the ratio of inflation rates. Hence:

$$\frac{S^{USD/GBP}_{t}}{S^{USD/GBP}_{t-1}}=\frac{{P^{USD}_{t}}/{P^{USD}_{t-1}}}{{P^{GBP}_{t}}/{P^{GBP}_{t-1}}}$$

Therefore if inflation in the UK is larger than inflation in the US, the British Pound would be expected to depreciate to maintain international purchasing parity. We can observe the consequences of the movement as individuals, we can buy product X in the US ($X^{US}$) or in the UK ($X^{UK}$). And let's assume the exchange rate is such that the price in terms of Pounds is the same:

At $t$:

$$X^{US}/S^{USD/GBP}=X^{US \rightarrow GBP} \space\space\space\space\space X^{US \rightarrow GBP}=X^{GBP}$$

At ${t+\scriptsize 1}$ there is inflation in the US but prices are fixed in the UK:

$$\uparrow X^{US}\space\space\space S^{USD/GBP}\rightarrow ?$$

If $\uparrow S^{USD/GBP}$ and its rise is proportional to the inflation impact then previous balance of $X^{US \rightarrow GBP}=X^{GBP}$ is conserved.

 

On the contrary, if $\downarrow S^{USD/GBP}$ and USD gets stronger:

$$\uparrow X^{US}/\downarrow S^{USD/GBP}=\uparrow X^{US \rightarrow GBP} \space\space\space\space\space X^{US \rightarrow GBP}>X^{GBP}$$

In this situation British citizens purchasing power is damaged with respect with the US. Such change of prices and rates would affect negatively the US exports and would improve the ones from the UK in the two countries' trade. Thus, testing the significance of inflation differentials between pairs is one the techniques in order to help predict next period's FX rate.

International Fisher effect

What Fisher's hypothesis suggests is that differences in nominal interest rates will explain changes in spot rates in the FX market. We first need to assume that the interest rate parity holds. This no-arbitrage condition determines that investors will be indifferent to deposit in the home country or in any foreign one as the difference in rates of lending and depositing will be offset by changes in the foreign exchange rate.

When relating Fisher's theory that inflation is equal to the difference of nominal rates with real rates with uncovered interest rate parity reasoning that no profit can be made by carry trading currencies we obtain the following:

 

$$\frac{E(S^{USD/GBP}_{t+1})}{S^{USD/GBP}_{t}} - 1= \frac{i_{US}-i_{GB}}{1+i_{GB}}=E(\xi )$$ Where:

 

• $E(S^{USD/GBP}_{t+1})$ is the expected future spot rate for the pair USD/GBP.

   

• $S^{USD/GBP}_{t}$ is today's rate.

   

• $i_{US}$ is the nominal rate in the US.

   

• $i_{GB}$ is the nominal rate in Great Britain.

   

• $E(\xi )$ is the expected rate of change in the FX rate.

   

As we have seen, both interest rates and inflation play an important role in international finance theories. Therefore we may expect some influence on our goal to forecast future changes in the rate.

Let's test them!

We will first import some libraries and define tickers and labels for the data:

import pandas_datareader as pdr
import numpy as np
import datetime
import pandas as pd
import warnings
warnings.filterwarnings('ignore')

start=datetime.datetime(1980,1,1)
end=datetime.datetime(2016,12,31)

#Defining data to download and readable names to change afterwards
tickers = ['DEXJPUS','DEXUSEU','DEXUSUK']
change_names_fx=['JPYUSD','USDEUR','USDGBP']
tickers_funda=['BPBLTT01EZQ637N','BPBLTT01JPQ637N','BPBLTT01GBQ637N','BPBLTT01USQ636N','INTDSRJPM193N',
               'IRLTLT01JPM156N','INTDSREZQ193N','IRLTLT01EZM156N','FEDFUNDS','DGS10','INTDSRGBM193N',
              'IRLTLT01GBM156N','FPCPITOTLZGJPN','FPCPITOTLZGEMU','FPCPITOTLZGGBR','FPCPITOTLZGUSA']
change_names_funda=['CB EA','CB JP','CB UK','CB US','Rate JP','10Y JP','Rate EUR','10Y EUR',
                    'Rate US','10Y US','Rate UK','10Y UK','Infl JP','Infl EUR','Infl UK','Infl US']

In order to have an easy access to data, we create a function to get data from the FRED and label it in a recognizable way.

#We define the function to take data from FRED


def get_data_from_fred(start,end,tickers,tickers_funda):
    
    main_df=pd.DataFrame()
    #We loop in tickers
    for n in range(0,len(tickers)):
              
               
        ticker_compile = pdr.DataReader(tickers[n], 'fred',start, end) 
        main_df=main_df.join(ticker_compile,how='outer')
        
    if len(tickers_funda)>0:    
        
        for n in range(0,len(tickers_funda)):                
            
           
            ticker_compile = pdr.DataReader(tickers_funda[n], 'fred',start, end)
            main_df=main_df.join(ticker_compile,how='outer')
        
    main_df.to_csv('Data_joined.csv')        
    
         
                              

get_data_from_fred(start,end,tickers,tickers_funda)

We exported the data to a CSV file so that we can explore the data and prepare for the preprocessing and formatting. That is exactly what we do in next cell:

import math

#Load the file with the data into a DataFrame

main_df=pd.read_csv('Data_joined.csv',index_col=0)

#Replace null values with average of previous and next value
for n in range(len(tickers)):
    for z in range(len(main_df.iloc[:,n])):
        if z==0:
            if(pd.isnull(main_df.iloc[z,n])):
                main_df.iloc[z,n]=main_df.iloc[z+1,n]
        if z>0:            
            if(pd.isnull(main_df.iloc[z,n])):
                main_df.iloc[z,n]=(main_df.iloc[z-1,n]+main_df.iloc[z+1,n])/2

#Replace missing values of data that is issued less frequently                
for n in range(len(tickers),len(tickers)+len(tickers_funda)):
    for z in range(len(main_df.iloc[:,n])):        
        if(pd.isnull(main_df.iloc[z,n])):
            main_df.iloc[z,n]=main_df.iloc[z-1,n]
            
#Replace names into a readable format and calculate rates from USD perspective

main_df.columns=change_names_fx+change_names_funda

main_df['USDEUR']=1/main_df['USDEUR']

main_df['USDGBP']=1/main_df['USDGBP']

main_df.rename(columns={'USDEUR':'EURUSD','USDGBP':'GBPUSD'},inplace=True)

#Calculate USD strength against JPY and GBP
main_df['Trend JP']=0
main_df['Trend GBP']=0

for x in range(0,len(main_df['EURUSD'])): 
        
    main_df['Trend JP'].iloc[x]=(main_df['JPYUSD'].iloc[x]/main_df['JPYUSD'].iloc[0])
    main_df['Trend GBP'].iloc[x]=(main_df['GBPUSD'].iloc[x]/main_df['GBPUSD'].iloc[0])
    
#Extra formatting for EUR (data from 2000 on), same as before, strength of USD against EUR  

main_df_EUR=main_df['2000-01-01'::].copy()
main_df_EUR['Trend EUR']=0

for x in range(0,len(main_df_EUR['EURUSD'])):  
      
    main_df_EUR['Trend EUR'].iloc[x]=(main_df_EUR['EURUSD'].iloc[x]/main_df_EUR['EURUSD'].iloc[0])    
    
#Formatting for Q and Y frequencies
main_df.index = pd.to_datetime(main_df.index)
main_df_Q=main_df.resample('Q').mean()
main_df_Q=main_df_Q.reset_index()
main_df_Q['DATE'] = main_df_Q['DATE'].dt.to_period("Q")
main_df_Q=main_df_Q.set_index('DATE')

main_df_Y=main_df.resample('A').mean()
main_df_Y=main_df_Y.reset_index()
main_df_Y['DATE'] = main_df_Y['DATE'].dt.to_period("A")
main_df_Y=main_df_Y.set_index('DATE')

#EUR
main_df_EUR.index = pd.to_datetime(main_df_EUR.index)
main_df_Q_EUR=main_df_EUR.resample('Q').mean()
main_df_Q_EUR=main_df_Q_EUR.reset_index()
main_df_Q_EUR['DATE'] = main_df_Q_EUR['DATE'].dt.to_period("Q")
main_df_Q_EUR=main_df_Q_EUR.set_index('DATE')

main_df_Y_EUR=main_df_EUR.resample('A').mean()
main_df_Y_EUR=main_df_Y_EUR.reset_index()
main_df_Y_EUR['DATE'] = main_df_Y_EUR['DATE'].dt.to_period("A")
main_df_Y_EUR=main_df_Y_EUR.set_index('DATE')

Now we are ready to see how the USD moved with respect the currencies in our analysis (GBP,JPY and EUR).

Note:Index at 1.

#Plot strength

import matplotlib.pyplot as plt

main_df['Trend EUR']=main_df_EUR['Trend EUR']

import plotly.plotly as py
import plotly
import plotly.graph_objs as go 
from datetime import datetime
import pandas_datareader.data as web


line1 = go.Scatter(
     x = main_df_EUR.index, 
    y = main_df_EUR['Trend EUR'], 
    name = "EUR",   
)

line2 = go.Scatter(
     x = main_df.index, 
    y = main_df['Trend GBP'], 
    name = "GBP",   
)

line3 = go.Scatter(
     x = main_df.index, 
    y = main_df['Trend JP'], 
    name = "JP",   
)

data = [line1,line2,line3]
layout = dict(
    title='USD strength',
    xaxis=dict(
        rangeselector=dict(
            buttons=list([        
                dict(count=1,
                    label='YTD',
                    step='year',
                    stepmode='todate'),
                dict(count=1,
                    label='1y',
                    step='year',
                    stepmode='backward'),
                dict(step='all')
            ])
        ),
        rangeslider=dict(),
        type='date'
    )
)

fig = dict(data=data, layout=layout)
py.iplot(fig)

For our regressions, we need to calculate the differentials for the currencies:

#Calculation of differentials across currencies
###EUR###
main_df_Y_EUR['% Change EURUSD']=0
main_df_Y_EUR['Dif Rates USD-EUR']=0
main_df_Y_EUR['Dif Inf USD-EUR']=0

for x in range(0,len(main_df_Y_EUR['EURUSD'])):
    if x==(len(main_df_Y_EUR['EURUSD'])-1):
        main_df_Y_EUR['% Change EURUSD'].iloc[x]=0
    else:
        #Calculate change happened that year with those years' variables
        main_df_Y_EUR['% Change EURUSD'].iloc[x]=(main_df_Y_EUR['EURUSD'].iloc[x+1]/main_df_Y_EUR['EURUSD'].iloc[x])-1
        main_df_Y_EUR['Dif Rates USD-EUR'].iloc[x]=(main_df_Y_EUR['Rate US'].iloc[x]-main_df_Y_EUR['Rate EUR'].iloc[x])
        #Inflation values in that year are known from last year (we do not know current inflation so t-1)
        main_df_Y_EUR['Dif Inf USD-EUR'].iloc[x]=(main_df_Y_EUR['Infl US'].iloc[x-1]-main_df_Y_EUR['Infl EUR'].iloc[x-1])
        
###JPY###
main_df_Y['% Change JPYUSD']=0
main_df_Y['Dif Rates USD-JP']=0
main_df_Y['Dif Inf USD-JP']=0
###Machine learning analysis###
main_df_Y['Dif 10Y Rates USD-JP']=0
main_df_Y['Dif CB USD-JP']=0



for x in range(0,len(main_df_Y['JPYUSD'])):
    if x==(len(main_df_Y['JPYUSD'])-1):
        main_df_Y['% Change JPYUSD'].iloc[x]=0
    else:
        #Calculate change happened that year with those years' variables
        main_df_Y['% Change JPYUSD'].iloc[x]=(main_df_Y['JPYUSD'].iloc[x+1]/main_df_Y['JPYUSD'].iloc[x])-1
        main_df_Y['Dif Rates USD-JP'].iloc[x]=(main_df_Y['Rate US'].iloc[x]-main_df_Y['Rate JP'].iloc[x])
        main_df_Y['Dif 10Y Rates USD-JP'].iloc[x]=(main_df_Y['10Y US'].iloc[x]-main_df_Y['10Y JP'].iloc[x])
        #Inflation values in that year are known from last year (we do not know current inflation so t-1)
        main_df_Y['Dif Inf USD-JP'].iloc[x]=(main_df_Y['Infl US'].iloc[x-1]-main_df_Y['Infl JP'].iloc[x-1])
        main_df_Y['Dif CB USD-JP'].iloc[x]=(main_df_Y['CB US'].iloc[x-1]-main_df_Y['CB JP'].iloc[x-1])
        
###GBP###
main_df_Y['% Change GBPUSD']=0
main_df_Y['Dif Rates USD-UK']=0
main_df_Y['Dif Inf USD-UK']=0

for x in range(0,len(main_df_Y['GBPUSD'])):
    if x==(len(main_df_Y['GBPUSD'])-1):
        main_df_Y['% Change GBPUSD'].iloc[x]=0
    else:
        #Calculate change happened that year with those years' variables
        main_df_Y['% Change GBPUSD'].iloc[x]=(main_df_Y['GBPUSD'].iloc[x+1]/main_df_Y['GBPUSD'].iloc[x])-1
        main_df_Y['Dif Rates USD-UK'].iloc[x]=(main_df_Y['Rate US'].iloc[x]-main_df_Y['Rate UK'].iloc[x])
        #Inflation values in that year are known from last year (we do not know current inflation so t-1)
        main_df_Y['Dif Inf USD-UK'].iloc[x]=(main_df_Y['Infl US'].iloc[x-1]-main_df_Y['Infl UK'].iloc[x-1])
        
        
        
    

Let's regress in all pairs:

#EURUSD regression Rates and Inflation
Reg_EURUSD_Y_Dependent=main_df_Y_EUR[0:-1]['% Change EURUSD']
Reg_EURUSD_Y_Variables=main_df_Y_EUR[0:-1][['Dif Rates USD-EUR','Dif Inf USD-EUR']]

import statsmodels.api as sm


Reg_EURUSD_Y_Variables=sm.add_constant(Reg_EURUSD_Y_Variables)
result_EURUSD=sm.OLS(Reg_EURUSD_Y_Dependent,Reg_EURUSD_Y_Variables).fit()

#Regression JPYUSD
Reg_JPYUSD_Y_Dependent=main_df_Y[0:-1]['% Change JPYUSD']
Reg_JPYUSD_Y_Variables=main_df_Y[0:-1][['Dif Rates USD-JP','Dif Inf USD-JP']]


Reg_JPYUSD_Y_Variables=sm.add_constant(Reg_JPYUSD_Y_Variables)
result_JPYUSD=sm.OLS(Reg_JPYUSD_Y_Dependent,Reg_JPYUSD_Y_Variables).fit()


#GBPUSD Regression, unfortunately we only have all data for both countries from 1990
Reg_GBPUSD_Y_Dependent=main_df_Y['1990'::]['% Change GBPUSD']
Reg_GBPUSD_Y_Variables=main_df_Y['1990'::][['Dif Rates USD-UK','Dif Inf USD-UK']]


Reg_GBPUSD_Y_Variables=sm.add_constant(Reg_GBPUSD_Y_Variables)
result_GBPUSD=sm.OLS(Reg_GBPUSD_Y_Dependent,Reg_GBPUSD_Y_Variables).fit()

print(result_EURUSD.summary())
print(result_JPYUSD.summary())
print(result_GBPUSD.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:        % Change EURUSD   R-squared:                       0.010
Model:                            OLS   Adj. R-squared:                 -0.142
Method:                 Least Squares   F-statistic:                   0.06738
Date:                Wed, 24 Jan 2018   Prob (F-statistic):              0.935
Time:                        17:46:15   Log-Likelihood:                 17.723
No. Observations:                  16   AIC:                            -29.45
Df Residuals:                      13   BIC:                            -27.13
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
=====================================================================================
                        coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------
const                -0.0041      0.040     -0.102      0.920      -0.090       0.082
Dif Rates USD-EUR     0.0052      0.026      0.198      0.846      -0.052       0.062
Dif Inf USD-EUR       0.0052      0.049      0.108      0.916      -0.100       0.110
==============================================================================
Omnibus:                        3.230   Durbin-Watson:                   1.663
Prob(Omnibus):                  0.199   Jarque-Bera (JB):                1.279
Skew:                           0.609   Prob(JB):                        0.528
Kurtosis:                       3.659   Cond. No.                         4.61
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
                            OLS Regression Results                            
==============================================================================
Dep. Variable:        % Change JPYUSD   R-squared:                       0.143
Model:                            OLS   Adj. R-squared:                  0.091
Method:                 Least Squares   F-statistic:                     2.744
Date:                Wed, 24 Jan 2018   Prob (F-statistic):             0.0790
Time:                        17:46:15   Log-Likelihood:                 32.937
No. Observations:                  36   AIC:                            -59.87
Df Residuals:                      33   BIC:                            -55.12
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
====================================================================================
                       coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------
const               -0.0874      0.036     -2.455      0.020      -0.160      -0.015
Dif Rates USD-JP     0.0013      0.008      0.171      0.865      -0.014       0.017
Dif Inf USD-JP       0.0290      0.015      1.970      0.057      -0.001       0.059
==============================================================================
Omnibus:                        1.453   Durbin-Watson:                   1.319
Prob(Omnibus):                  0.484   Jarque-Bera (JB):                0.536
Skew:                           0.071   Prob(JB):                        0.765
Kurtosis:                       3.581   Cond. No.                         10.2
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
                            OLS Regression Results                            
==============================================================================
Dep. Variable:        % Change GBPUSD   R-squared:                       0.086
Model:                            OLS   Adj. R-squared:                  0.010
Method:                 Least Squares   F-statistic:                     1.126
Date:                Wed, 24 Jan 2018   Prob (F-statistic):              0.341
Time:                        17:46:15   Log-Likelihood:                 34.996
No. Observations:                  27   AIC:                            -63.99
Df Residuals:                      24   BIC:                            -60.11
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
====================================================================================
                       coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------
const                0.0071      0.018      0.392      0.699      -0.030       0.045
Dif Rates USD-UK    -0.0031      0.008     -0.404      0.689      -0.019       0.013
Dif Inf USD-UK      -0.0139      0.011     -1.255      0.222      -0.037       0.009
==============================================================================
Omnibus:                        2.935   Durbin-Watson:                   1.627
Prob(Omnibus):                  0.231   Jarque-Bera (JB):                2.075
Skew:                           0.679   Prob(JB):                        0.354
Kurtosis:                       3.013   Cond. No.                         3.58
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

We only observe the inflation differential of the JPY/USD pair as significant factor in our regressions. It has positive sign, consequently when inflation in the US is higher than in Japan we expect the Dollar to get stronger with respect the Yen.

How can we explain this deviation from theoretical frameworks?

Market fluctuations are not always a reflection of fundamentals, eventually, those movements are expectations that are projected to the underlying tradable good.

That is why, when a country experiences inflation, like in this case the US, investors might expect central bank to raise rates and thus, will increase demand for US dollars. The long term empirical evidence shows how positive inflation differentials will depreciate the currency, following purchasing power theory.

Machine learning approach through technical analysis

Technical analysis

Technical analysis is used to forecast direction of prices from past data through its prices, ratios, moving averages, volumes and chartism among others. It follows behavioral economics theories that defend the seeking of patterns biases investors from efficient unpredictable pricing and gives room for pattern-recognition strategies. If a large enough amount of investors believe in technical analysis then it will be present in trading strategies and thus, should work if predicted correctly.

There is an extensive offer of techniques, the most famous ones are the chart patterns as the head and shoulders double top or bottom rebound, the crossing moving averages and lines of support, resistance or channels.

Technical analysis attempts to confine the psychology of crowds and the cycles of optimism and fear. It relies on the fact that history repeats itself in the markets and that it is possible to read those trends.

                                                          Example of moving averages analysis.

Nevertheless, pattern recognition is being greatly overcome by machines nowadays. The purpose of our analysis is to test how several machine learning algorithms would behave when facing the task of detecting pattern in our data. The data will be exclusively daily average Ask and Bid prices for the JPY/USD and the EUR/USD pairs. Equally, the simulations for back-testing will be performed from the point of view of a US investor.

Trading horizon is daily, having to decide whether we hold USD, we buy JPY(EUR) or we sell JPY(EUR). For that, we provided the algorithm with training data before performing with unseen backtests. In this training data, we implement a signal feature with the historical return of t+3. This way, by observing what kind of trend was happening for the different outcomes in the next three days, the algorithm will be able to relate it when in the test data, assuring a longer term trend.

Following, we will explain how the process works in detail:

We start by downloading the data from Quandl and calculating and plotting the returns.

import quandl
import matplotlib.pyplot as plt
import seaborn as sns
from IPython.core.display import display
from collections import Counter
%matplotlib inline

df_technical=quandl.get("PERTH/USD_JPY_D", authtoken="Z-5Q1MtTbYxMUDfrvVJw",end_date="2015-12-31")

#Define and calculate nominal return and normalized return
df_technical['Return Nominal'] = df_technical['Bid Average']/((df_technical['Ask Average']).shift(-1))-1
df_technical['Return'] = df_technical['Bid Average'] - (df_technical['Ask Average'].shift(-1))
return_rescale = df_technical['Return'].max() - df_technical['Return'].min()
df_technical['Return'] = df_technical['Return'] / return_rescale

#Return from Dollar perspective
plt.style.use('fivethirtyeight')
ax=df_technical.plot(y='Return Nominal', figsize=(10,4),lw=1,ylim=(-0.06,0.06))
ax.set_title("JPY Return")
ax.set_xlabel("Date")
ax.set_ylabel("Daily %")
plt.show()

We see how the Asian crisis in 1997 and the Financial Crisis in 2008 affect the volatility of returns. Next, we need to create our features, in the DataFrame under here, we create a dummy per row indicating whether the JPY is going to be stronger next day, in that case we want to buy JPY today to enjoy of the return in USD.

# We create a signal with dummy variables of profit or loss.

#We shift Return one row above
df_technical['Dummy'] = df_technical['Return']
#Return positive means stronger JPY, therefore we want to be holding JPY before that moment in order to achieve
#profits in USD
df_technical['Dummy'] = df_technical['Dummy'].apply(lambda x: 1 if x>0.0 else 0)
# df.dropna(inplace=True)
df_technical.head()

Rank	Currency	Share
1	USD	87.6%
2	EUR	31.4%
3	JPY	21.6%
4	GBP	12.8%
5	AUD	6.9%

	Bid High	Ask High	Bid Low	Ask Low	Bid Average	Ask Average	Return Nominal	Return	Dummy
Date
1991-06-21	139.01	139.27	138.33	138.56	138.88	139.13	-0.003087	-0.033205	0
1991-06-22	139.18	139.40	138.99	139.22	139.08	139.31	-0.003868	-0.041699	0
1991-06-24	139.38	139.64	139.18	139.58	139.32	139.62	0.000718	0.007722	1
1991-06-25	139.01	139.27	138.87	139.12	138.95	139.22	0.000288	0.003089	1
1991-06-26	138.21	138.98	138.09	138.85	138.15	138.91	0.000145	0.001544	1